Dynamic modeling of immobilized cell reactor: application to ethanol fermentation

A mathematical model has been developed for the unsteady-state operation of an immobilized cell reactor. The substrate solution flows through a mixed-flow reactor in which cells immobilized in gel beads are retained. The substrate diffuses from the external surface of the gel beads to some internal location where reaction occurs. The product diffuses from the gel beads into liquid medium which flows out of the reactor. The model combines simultaneous diffusion and reaction, as well as cell growth, and it can predict how the rates of substrate consumption, product formation, and cell growth vary with time and with initial conditions. Ethanol fermentation was chosen as a representative reaction in the immobilized cell reactor, and numerical calculations were carried out. Excellent agreement was observed between model predictions and experimental data available in the literature.     

Growth and substrate consumption of Nitrobacter agilis cells immobilized in carrageenan: part 2. Model evaluation

A dynamic model that predicts substrate and biomass concentration profiles across gel beads and from that the overall substrate consumption rate by the gel beads containing growing cells was evaluated with immobilized Nitrobacter agilis cells in an airlift loop reactor with oxygen as the limiting substrate. The model predictions agreed well with the observed oxygen consumption rates at three different liquid phase oxygen concentrations. Image analysis showed that 90% of the immobilized cells after 42 days of cultivation was situated in the outer shells in a film of 140 mum, while the bead radius was about 1 mm. The maximum biomass concentration in the outmost film of 56 mum was 11 kg . m(-3) gel.     

Oxygen diffusivity in gel beads containing viable cells

This article proposes a simple steady-state method for measuring the effective diffusion coefficient of oxygen (D(e)) in gel beads entrapping viable cells. We applied this method to the measurement of D(e) in Ca- and Ba-alginate gel beads entrapping Saccharomyces cerevisiae and Pseudomonas ovalis. The diffusivity of oxygen through gel beads containing viable cells was measured within an accuracy of +/-7% and found not to be influenced by cell density (0-30 g/L gel), cell type, and cell viability in gel beads. The oxygen diffusivity in the Ca-alginate gel beads was superior to that of the Ba-alginate gel beads, and the D(e) in the Ca-alginate gel beads nearly equalled the molecular diffusion coefficient in the liquid containing the gel beads. The oxygen concentration profile in a single Ca-alginate gel bead was calculated and compared to the distribution of mycelia of Aspergillus awamori grown in that gel bead. This procedure indicated that the oxygen concentration profile is useful for the estimation of the thickness of the cell layer in a gel bead. Numerical investigation revealed that high effectiveness factors, greater than 0.8, could be obtained using microgel beads with a radius of 0.25 mm.     

Mass transfer effects on the reaction rate for heterogeneously distributed immobilized yeast cells

Here we examine the efficiency of different immobilized cell gradients applied to immobilized Saccharomyces cerevisiae fermenting glucose to ethanol. We developed a simulation model to fully study the competing effects of mass transfer hindrance and kinetics. It is based on a diffusion-reaction model and can be used to analyze the different cell concentration profiles inside an immobilized gel bead, in terms of effectiveness factors, productivity, and mass flux. The internal diffusion coefficient, which varies with the local cell concentration, as well as the external mass transfer, is taken into account when describing the efficiency. Although the diffusion hindrance is greater at higher cell concentrations, high cell concentration is still advantageous in the present case because the increase in reaction rate outweighs the diffusion hindrance. Thus, high cell concentrations contribute to increased productivity. The influence of the cell concentration gradient on the efficiency of the beads is negligible. Within the range of cell profiles studied it has been established that the location of the cells within the bead is of lesser importance. However, a steep cell gradient increases the importance of the external mass transfer.     

An investigation of bioreactor performance for the production of recombinant protein in immobilized and suspended Escherichia coli

The performance of packed bed (PBR) and modified bubble tank (MBTR) reactors was compared with respect to recombinant protein (β-galactosidase) production by suspended and immobilized E. coli. The MBTR was superior to the PBR due to easy operation and higher protein production. Gas-liquid mass transfer was not affected by the presence of gel beads, and there were no internal or external oxygen diffusion limitations in either reactor. High substrate concentration, small bead size, low cell densities, and similar values of effective diffusion coefficient of oxygen in water and in alginate may have decreased the internal mass transfer limitations.     

Effects of temperature and shear on the activity of acid phosphatase in a tubular membrane reactor

The effect of temperature on the activity of acid phosphatase [orthophosphoric-monoester phosphohydrolase (acid optimum), EC 3.1.3.2] immobilized as a gel layer on the inner wall of ultrafiltration tubular membranes by both copolymerization/gelation and cogelation has been investigated. Both forms of gel-immobilized enzyme showed fairly good stability, the activation energy of their inactivation being significantly lower than that of the free enzyme and of the heat denaturation of proteins in general. The shear effect on the cogelled enzyme was also studied at different temperatures and Reynolds numbers. The results indicated that the cogelled enzyme is a more convenient form for continuous operation in the tubular membrane reactor (TMR), a reactor configuration particularly suitable for industrial applications.     

Mathematical modeling of diffusion and reaction in the hydrolysis of vegetable protein in an immobilized enzyme recycle reactor

Experimental investigation is by far the most effective approach for studying the behavior of physical systems. However, an enzymatic solubilization of vegetable protein is a complex combination of intrinsic problems, of which many are not easily adaptable to experimental investigation. Experimental designs to study enzyme vegetable protein reactions yield data which describe the extramembraneous activity of the immobilized enzyme. In a continuous recycle immobilized enzyme reactor, the microenvironment concentration of the substrate or product in the membrane phase, or the concentrations along the reactor axial length in the bulk phase are not discernible to the experimenter. However, the knowledge of such concentration profiles is important in weighing the significance of such factors as intermembrane diffusion, enzyme loading, wet membrane size, and the mode of operation of the reactor. The simulation of mathematical models, which describe the physical system within the constraints imposed, yields information which is vital to the understanding of the process occurring in the reactor. The kinetics and diffusion of an immobilized thermophilic Penicillium duponti enzyme at pH 3.4-3.7 and 50 degrees C was modeled mathematically. The kinetic parameters were evaluated by fitting a model to experimental data using nonlinear regression analysis. Simulation profiles of the effects of reactor geometry, substrate concentration, membrane thickness, and enzyme leading on the hydrolysis rate are presented. From the profiles generated by the mathematical model, the best operational reactor strategy is recommended.     

Role of nutrient supply on cell growth in bioreactor design for tissue engineering of hematopoietic cells

In the present study, a dynamic mathematical model for the growth of granulocyte progenitor cells in the hematopoietic process is developed based on the principles of diffusion and chemical reaction. This model simulates granulocyte progenitor cell growth and oxygen consumption in a three-dimensional (3-D) perfusion bioreactor. Material balances on cells are coupled to the nutrient balances in 3-D matrices to determine the effects of transport limitations on cell growth. The method of volume averaging is used to formulate the material balances for the cells and the nutrients in the porous matrix containing the cells. All model parameters are obtained from the literature. The maximum cell volume fraction reached when oxygen is depleted in the cell layer at 15 days and is nearly 0.63, corresponding to a cell density of 2.25 x 10(8) cells/mL. The substrate inhibition kinetics for cell growth lead to complex effects with respect to the roles of oxygen concentration and supply by convection and diffusion on cell growth. Variation in the height of the liquid layer above the cell matrix where nutrient supply is introduced affected the relative and absolute amounts of oxygen supply by hydrodynamic flow and by diffusion across a gas permeable FEP membrane. Mass transfer restrictions of the FEP membrane are considerable, and the supply of oxygen by convection is essential to achieve higher levels of cell growth. A maximum growth rate occurs at a specific flow rate. For flow rates higher than this optimal, the high oxygen concentration led to growth inhibition and for lower flow rates growth limitations occur due to insufficient oxygen supply. Because of the nonlinear effects of the autocatalytic substrate inhibition growth kinetics coupled to the convective transport, the rate of growth at this optimal flow rate is higher than that in a corresponding well-mixed reactor where oxygen concentration is set at the maximum indicated by the inhibitory kinetics.     

Determination of effective diffusion coefficients and distribution constants in polysaccharide gels with non-steady-state measurements

A non-steady-state method has been used for determining the effective diffusion coefficient, D(e), and a distribution constant, K(i), of small molecules in alginate gel beads. A mathematical model based on Pick's law and includingexternal film diffusion resistance describe the diffusion process. Criticalexperimental parameters for the estimation of D(e) and K(i), for both one- and two-parameter methods were the initial solute concentration in the bulk liquid, the void fraction inthe reactor, and the experimental starting point. In our analysis, the two-parameter method is preferable. Incorporation of an estimate of the film resistance into the overall model increased the estimated values of D(e) significantly and improved the stability of the term over a range of reactor agitation rates. (c) 1995 John Wiley & Sons Inc.     

An immobilized cell reactor with simultaneous product separation. I. Reactor design and analysis

A four-phase reactor-separator (gas, liquid, solid, and immobilized catalyst) is proposed for fermentations characterized by a volatile product and nonvolatile substrate.In this reactor, the biological catalyst is immobilized onto a solid column packing and contacted by the liquid containing the substrate.A gas phase is also moved through the column to strip the volatile product into the gas phase. The Immobilized Cell Reactor-Separator (ICRS) consists of two basic gas-liquid flow sections: a cocurrent "enricher" followed by a countercurrent-"stripper".In this article, an equilibrium stage model of the reactor is developed to determine the feasibility and important operational variables of such a reactor-separator. The ICRS concept is applied to the ethanol from whey lactose fermentation using some preliminary immobilized cell reactor performance data. A mathematical model for a steady-state population based on an adsorbed monolayer of cells is also developed for the reactor. The ICRS model demonstrated that the ICRS should give a significant increase in reactor productivity as compared to an identically sized Immobilized Cell Reactor (ICR) with no separation. The gas-phase separation of the product also allows fermentation of high inlet substrate concentrations. The model is used to determine the effects of reactor parameters on ICRS performance including temperature, pressure, gas flow rates, inlet substrate concentration, and degree of microbial product inhibition.     

Effect of growing conditions of recombinantE.coli in carrageenan gel beads upon biomasse production and plasmid stability

Summary The biomass production and the plasmid stability of immobilizedE. coli cells in K-carrageenan gel beads were investigated in continuous cultures. Several factors, such as inoculum size, gel bead volume and gel concentration were examined in order to increase the cell concentration inside the immobilized cell reactor, and therefore to increase the overall productivity.     

Enhancement and stabilization of the production of glucoamylase by immobilized cells of Aureobasidium pullulans in a fluidized-bed reactor

Summary Glucoamylase production by Aureobasidium pollulans A-124 was compared in free-living cells, cells immobilized in calcium alginate gel beads aerated on a rotary shaker (agitation rate 150 rpm), and immobilized cells aerated in an air bubble column reactor. Fermentation conditions in the bioreactor were established for bead concentration, substrate (starch) concentration, calcium chloride addition to the fermentation medium, and rate of aeration. Production of glucoamylase was optimized at approximately 1.5 units of enzyme activity/ml medium in the bioreactor under the following conditions: aeration rate, 2.0 vol air per working volume of the bioreactor (280 ml) per minute; gel bead concentration, 30% of the working volume; substrate (starch) concentration, at 0.3% (w/v); addition of calcium chloride to the medium at a final concentration of 0.01 M. Productivity levels were stabilized through the equivalent of ten batches of medium with the original inoculum of immobilized beads. Offprint requests to: M. Petruccioli     

Effect of initial biomass concentration on the growth of immobilized Nitrosomonas europaea

Nitrosomonas europaea was immobilized in carrageenan-gel beads with a low and a high biomass concentration (100-fold difference). Under growth conditions in a continuous air-lift loop reactor, a low initial concentration yielded a few large micro-colonies per bead, whereas a high initial biomass concentration resulted in many small micro-colonies per bead. The macroscopic consumption rate of the latter was three times higher under the circumstances applied. This is also predicted by our colony-expansion model when diffusion limitation over the micro-colonies is incorporated. This model also predicts that diffusion limitation over the ultimate colonies is negligible when the initial biomass concentration exceeds 0.5 kg·m^–3 of carrageenan gel.     

Rigorous model for spherical cell-support aggregate

The activity of immobilized cell-support particle aggregates is influenced by physical and biochemical elements, mass transfer, and physiology. Accordingly, the mathematical model discussed in this study is capable of predicting the steady state and transient concentration profiles of the cell mass and substrate, plus the effects of the substrate and product inhibition in an immobilized cell-support aggregate. The overall mathematical model is comprised of material balance equations for the cell mass, major carbon source, dissolved oxygen, and non-biomass products in a bulk suspension along with a single particle model. A smaller bead size and higher substrate concentration at the surface of the particle, resulted in a higher supply of the substrate into the aggregate and consequently a higher biocatalyst activity.     

Modeling of an aerobic biofilm reactor with double-limiting substrate kinetics: bifurcational and dynamical analysis

A mathematical model of an aerobic biofilm reactor is presented to investigate the bifurcational patterns and the dynamical behavior of the reactor as a function of different key operating parameters. Suspended cells and biofilm are assumed to grow according to double limiting kinetics with phenol inhibition (carbon source) and oxygen limitation. The model presented by Russo et al. is extended to embody key features of the phenomenology of the granular‐supported biofilm: biofilm growth and detachment, gas–liquid oxygen transport, phenol, and oxygen uptake by both suspended and immobilized cells, and substrate diffusion into the biofilm. Steady‐state conditions and stability, and local dynamic behavior have been characterized. The multiplicity of steady states and their stability depend on key operating parameter values (dilution rate, gas–liquid mass transfer coefficient, biofilm detachment rate, and inlet substrate concentration). Small changes in the operating conditions may be coupled with a drastic change of the steady‐state scenario with transcritical and saddle‐node bifurcations. The relevance of concentration profiles establishing within the biofilm is also addressed. When the oxygen level in the liquid phase is <10% of the saturation level, the biofilm undergoes oxygen starvation and the active biofilm fraction becomes independent of the dilution rate. © 2011 American Institute of Chemical Engineers Biotechnol. Prog., 2011     

Biofilm development in a membrane-aerated biofilm reactor: effect of flow velocity on performance

The effect of liquid flow velocity on biofilm development in a membrane-aerated biofilm reactor was investigated both by mathematical modeling and by experiment, using Vibrio natriegens as a test organism and acetate as carbon substrate. It was shown that velocity influenced mass transfer in the diffusion boundary layer, the biomass detachment rate from the biofilm, and the maximum biofilm thickness attained. Values of the overall mass transfer coefficient of a tracer through the diffusion boundary layer, the biofilm, and the membrane were shown to be identical during different experiments at the maximum biofilm thickness. Comparison of the results with published values of this parameter in membrane attached biofilms showed a similar trend. Therefore, it was postulated that this result might indicate the mechanism that determines the maximum biofilm thickness in membrane attached biofilms. In a series of experiments, where conditions were set so that the active layer of the membrane attached biofilm was located close to the membrane biofilm interface, it was shown that the most critical effect on process performance was the effect of velocity on biofilm structure. Biofilm thickness and effective diffusivity influenced reaction and diffusion in a complex manner such that the yield of biomass on acetate was highly variable. Consideration of endogenous respiration in the mathematical model was validated by direct experimental measurements of yield coefficients. Good agreement between experimental measurements of acetate and oxygen uptake rates and their prediction by the mathematical model was achieved.     

Kinetic modeling of a multiple immobilized enzyme system. II. Application of the model

The mathematical model for the reaction sequence catalyzed by immobilized invertase and glucose oxidase discussed in the preceding article has been used successfully to duplicate experimental findings. In addition, it has been used as a tool for the simulation and prediction of effects derived from alterations to system-related and gel-related parameters. The effects of gel diffusivity on the overall conversion of sucrose substrate to reaction products was investigated through use of this model. Changes in the enzyme loading within a gel and the results of varying the ration of invertase activity to glucose activity were also evaluated. Through use of concentrations of the molecular species determined at the collocation points within a gel particle and in the bulk liquid phase, an estimate of the thickness of the diffusion boundary layer around the gel particle was determined which was in close agreement with values obtained from classical mass transfer relationships. For most of this study, the enzymes were coimmobilized within the same polymeric matrix. However, a number of tests were run with the enzymes immobilized individually and placed in separate reactors in a sequential reactor system. The experimental results from these tests were duplicated successfully by means of the model with little modification to the basic computer program. Such an example illustrates the potential flexibility of the model and its overall versatility.     

Co-immobilized Nitrosomonas europaea and Nitrobacter agilis cells: validation of a dynamic model for simultaneous substrate conversion and growth in kappa-carrageenan gel beads

A dynamic model for two microbial species immobilized in a gel matrix is presented and validated with experiments. The model characterizes the nitrification of ammonia with Nitrosomonas europaea and Nitrobacter agilis co-immobilized in K-carrageenan gel beads. The model consists of kinetic equations for the microorganisms and mass transfer equations for the substrates and products inside and outside the gel beads. The model predicts reactor bulk concentrations together with the substrate consumption rate, product formation, and biomass growth inside the gel beads as a function of time. A 50-day experiment with immobilized cells in a 3.3-dm(3) air-lift loop reactor was carried out to validate the model. The parameter values for the model were obtained from literature and separate experiments. The experimentally determined reactor bulk concentrations and the biomass distribution of the two microorganisms in the gel beads were well predicted by the model. A sensitivity analysis of the model for the given initial values indicated the most relevant parameters to be the maximum specific growth rate of the microorganisms, the diffusion coefficient of oxygen, and the radius of the beads. The dynamic model provides a useful tool for further study and possible control of the nitrification process. (c) 1994 John Wiley & Sons, Inc.     

Modeling of a Catalyzed Reaction Using Lipase Immobilized in a Poly(vinyl alcohol) Membrane

A mathematical model for the hydrolysis reaction of p‐nitro phenol laurate catalyzed by a lipase immobilized in a membrane was developed. In an earlier study this model reaction was found to show very different reaction rates when it was performed in aqueous micellar solution with free enzyme and with membrane immobilized enzyme. It was assumed that a local accumulation of substrate in the membrane is responsible for the observed rate enhancement. The conversion of p‐nitro phenol ester within the membrane was modeled by considering a combination of the convective flow through poly(vinyl alcohol) membrane pores, concentration polarization of substrate containing micelles at the membrane surface and the kinetics of the reaction with free enzymes. It was demonstrated that the model offered a comprehensive understanding of the interaction of the involved phenomena. The modeling results are in good agreement with the experimental data from 10 runs with different enzyme and substrate concentrations. The substrate concentration at the membrane surface increased by up to a factor of 3 compared to the feed concentration. This effect explains the observed rate enhancement. Moreover, the model was used to determine the unknown parameters, i.e., the intrinsic retention and the mass transfer coefficient, by fitting the model to the experimental data. The model may also be used to calculate the optimum operating conditions and design parameters of such a reactor.